Analytical study of critical magnetic field in a holographic superconductor

TL;DR

This paper analytically investigates the influence of external magnetic fields on holographic superconductors, revealing a Meissner-like effect and analyzing quantum phase transitions at zero temperature.

Contribution

It provides an analytical approach using Sturm-Liouville method to study magnetic effects and phase diagrams in holographic superconductors, highlighting new insights into their critical behavior.

Findings

Critical magnetic field coefficient depends on external magnetic field.

A Meissner-like effect is observed in holographic superconductors.

Critical charge density increases linearly with condensate dimension at zero temperature.

Abstract

We analytically sutdy the effect of external magnetic field in a Holographic superconductor by using Sturm-Liouville method. We estimate the coefficient of proportionality at critical temperature and find its denpendence on external magnetic field. By exploring phase diagrams of critical temperature and magnetic field for various condensates, we conclude that a Meissner-like effect is a general feature in Holographic superconductors. We also study the quantum phase transition at zero temperature and find that critical charge density increases linearly with the condensate dimension.